Unit 3 Topic 5: Earth geometry and time zones

Find the angular distance first: subtract latitudes or longitudes on the same side, add them on opposite sides, then multiply by 111.2 (and by cos of the latitude along a parallel).

A lesson for this topic

Paper 1 style: multiple choice

Question 1Paper 1 style

Which one of the following is a great circle on the Earth's surface?

Question 2Paper 1 style

Which one of the following statements about latitude and longitude is true?

Question 3Paper 1 style

A reef buoy is at 19.1°S, 147.8°E. What is its position in degrees and minutes?

Question 4Paper 1 style

Two towns lie on the meridian 146°E. One is at 19°15′S and the other is at 27°30′S. What is the angular distance between the towns?

Question 5Paper 1 style

Two islands lie on the meridian 130°E. One is at 12°36′N and the other is at 20°24′S. What is the distance between the islands along the meridian, correct to the nearest kilometre?

Question 6Paper 1 style

Town

A

is at 35°S, 18°E and town

B

is at 35°S, 86°W. What is the angular distance between

A

and

B

along the parallel of latitude 35°S?

Question 7Paper 1 style

Two towns lie on the parallel of latitude 27°30′S, at longitudes 139°E and 153°E. What is the distance between them along the parallel, correct to the nearest kilometre?

Question 8Paper 1 style

Four places are

A

(31°S, 116°E),

B

(31°S, 150°E),

C

(12°S, 131°E) and

D

(42°S, 131°E). Which one of the following statements is true?

Question 9Paper 1 style

A ship at 6°40′S sails due north along its meridian for 1500 km. What is its new latitude, correct to the nearest minute?

Question 10Paper 1 style

A light plane leaves an airstrip at 30°S, 120°E and flies due east along the parallel of latitude 30°S for 2500 km. What is its longitude when it lands, correct to the nearest degree?

Question 11Paper 1 style

Island

P

is at 40°N, 160°E and island

Q

is at 40°N, 150°W. A boat sails between them along the parallel 40°N the shorter way. How far does it sail, correct to the nearest kilometre?

Question 12Paper 1 style

Which one of the following statements is true?

Question 13Paper 1 style

The local times of two places, based on longitude alone, differ by 6 hours 40 minutes. What is the difference in their longitudes?

Question 14Paper 1 style

Town

A

is at longitude 150°E and town

B

is at longitude 45°W. Each town keeps the local time given by its longitude. When it is 20:00 Tuesday in town

A

, what is the time in town

B

Question 15Paper 1 style

Brisbane uses UTC+10 and does not use daylight saving. A town in South America uses UTC−3. When it is 18:30 Thursday in Brisbane, what is the time in the South American town?

Question 16Paper 1 style

Perth uses UTC+8 and does not use daylight saving. Sydney uses UTC+10, and daylight saving (one hour forward) is in effect. Ana rings her brother in Sydney at 21:30 Friday, Perth time. What is the date and time in Sydney?

Question 17Paper 1 style

A flight leaves Brisbane (UTC+10, no daylight saving) at 23:10 Monday, local time, and flies for 9 hours 35 minutes to Singapore (UTC+8, no daylight saving). What is the local time in Singapore when the flight lands?

Question 18Paper 1 style

A flight leaves Auckland at 21:30 Wednesday, local time, and flies east for 8 hours 45 minutes to Honolulu. Auckland is on UTC+12, and daylight saving (one hour forward) is in effect there. Honolulu is on UTC−10 and does not use daylight saving. What is the local time in Honolulu when the flight lands?

Question 19Paper 1 style

A town at longitude 100°E keeps the local time given by its longitude. A second place, also keeping the time given by its longitude, is 7 hours 20 minutes behind the town. What is the longitude of the second place?

Question 20Paper 1 style

A grand final starts at 14:30 Saturday in Melbourne, where daylight saving is in effect (UTC+11). It is shown live in Los Angeles, which is on UTC−7 with daylight saving in effect. What is the local time in Los Angeles when the match starts?

Question 21Paper 1 style

Kai lives in Townsville (UTC+10, no daylight saving). His cousin lives in Vancouver, which is on UTC−7 (this offset already includes daylight saving). The cousin can take calls between 18:00 and 21:00 Thursday, Vancouver time. At which Townsville time could Kai ring?

Question 22Paper 1 style

A ship crosses the International Date Line travelling east. Just before it crosses, the ship's clocks show 10:00 Tuesday. Which one of the following could be the ship's local date and time just after crossing?

Short response questions

Three weather stationsShort response · 5 marks

Weather station

P

is at 16°55′S, 145°45′E. Station

Q

is at 23°25′S, 145°45′E, and station

R

is at 16°55′S, 150°15′E.

(a) What is the angular distance between

P

and

Q

, in degrees? Give your answer as a decimal. [1]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(b) What is the distance between

P

and

Q

, correct to the nearest kilometre? [1]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(d) What is the distance between

P

and

R

along their parallel of latitude, correct to the nearest kilometre? [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

A research ship in the Southern OceanShort response · 7 marks

A research ship leaves point

A

at 42°S, 147°E and sails due east along the parallel of latitude 42°S, the shorter way, to point

B

at 42°S, 172°W. From

B

it sails due north along the meridian 172°W for 1500 km to point

C

(a) What is the angular distance from

A

B

, in degrees? [1]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(b) How far does the ship sail from

A

B

, correct to the nearest kilometre? [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

C

, in degrees south, correct to one decimal place? [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(d) Explain why the distance from

A

B

is less than

111.2 \times 41

km. [2]

0 words · a sentence or two

A flight across the International Date LineShort response · 6 marks

Brisbane uses UTC+10 and does not use daylight saving. Los Angeles uses UTC−8, and daylight saving (one hour forward) is in effect there for all of this trip. A flight leaves Brisbane at 11:40 Tuesday, Brisbane time, and flies east for 13 hours 25 minutes to Los Angeles.

(a) How many hours is Los Angeles behind Brisbane during this trip? [1]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(b) What is the local time in Los Angeles when the flight lands? [1]

0 words · a sentence or two

(d) The return flight leaves Los Angeles at 22:50 Friday, local time, and lands in Brisbane at 06:20 Sunday, local time. Daylight saving is still in effect in Los Angeles. How long is the return flight, in hours? [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

Longitude, time zones and daylight savingShort response · 6 marks

Town

Q

is at longitude 105°E and uses UTC+7. Town

R

is at longitude 60°W and uses UTC−3. Neither town uses daylight saving unless a part says so.

(a) Based on longitude alone, how many hours apart are the local times of

Q

and

R

? [2]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(b) Using the towns' UTC offsets, how many hours ahead of

R

Q

? [1]

Type fractions as 3/8, powers as x^2 and roots as sqrt(5).

(c) A concert in $R$ starts at 20:30 Wednesday, local time, and is shown live in $Q$ . What is the local time in $Q$ when it starts? [1]

(d) Later in the year, daylight saving begins in

R

and its clocks move forward one hour. The clocks in

Q

do not change. Explain what happens to the time difference between

Q

and

R

. [2]

0 words · a sentence or two